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 Documentation Ver 1.0.0 August 2011 by
 <a href="http://mmc.geofisica.unam.mx/luiggi">Luis M. de la Cruz</a> <br>
 <a href="http://mmc.geofisica.unam.mx"> GMMC </a> -
 <a href="http://www.geofisica.unam.mx/recnat/"> Depto. de Recursos Naturales </a> -
 <a href="http://www.geofisica.unam.mx"> Instituto de Geof&iacute;sica </a> -
 <a href="http://www.unam.mx"> UNAM </a><br>
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<div class="title">Examples/09FlowInPorousMedia/singlePhase2D.cpp</div>  </div>
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<a href="singlePhase2D_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 
<a name="l00024"></a>00024 <span class="preprocessor">#include &lt;iostream&gt;</span>
<a name="l00025"></a>00025 <span class="preprocessor">#include &lt;cmath&gt;</span>
<a name="l00026"></a>00026 <span class="preprocessor">#include &quot;Meshes/Uniform.hpp&quot;</span>
<a name="l00027"></a>00027 <span class="preprocessor">#include &quot;Equations/ScalarEquation.hpp&quot;</span>
<a name="l00028"></a>00028 <span class="preprocessor">#include &quot;Schemes/CDS.hpp&quot;</span>
<a name="l00029"></a>00029 <span class="preprocessor">#include &quot;Solvers/TDMA.hpp&quot;</span>
<a name="l00030"></a>00030 <span class="preprocessor">#include &quot;Utils/inout.hpp&quot;</span> 
<a name="l00031"></a>00031 <span class="preprocessor">#include &quot;Utils/num_utils.hpp&quot;</span>
<a name="l00032"></a>00032 <span class="preprocessor">#include &quot;Utils/GNUplot.hpp&quot;</span>
<a name="l00033"></a>00033 <span class="keyword">using namespace </span>Tuna;
<a name="l00034"></a>00034   
<a name="l00035"></a>00035 <span class="comment">// Scalar field in one dimension</span>
<a name="l00036"></a>00036 <span class="keyword">typedef</span> <a class="code" href="structTuna_1_1TunaArray.html#af3bcab5018eec3d7697c9fb03ad89157" title="Definition of big arrays to store scalar fields on meshes.">TunaArray&lt;double,2&gt;::huge</a> ScalarField2D;
<a name="l00037"></a>00037 
<a name="l00038"></a>00038 <span class="keywordtype">void</span> exactSolution(ScalarField2D &amp;T, <span class="keywordtype">double</span> hx, <span class="keywordtype">double</span> dx, <span class="keywordtype">double</span> PL, <span class="keywordtype">double</span> PR)
<a name="l00039"></a>00039 {
<a name="l00040"></a>00040   <span class="keywordtype">int</span> NI = T.ubound(firstDim);
<a name="l00041"></a>00041   <span class="keywordtype">int</span> NJ = T.ubound(secondDim);
<a name="l00042"></a>00042   <span class="keywordtype">double</span> coef = dx / hx;
<a name="l00043"></a>00043 
<a name="l00044"></a>00044   <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt;= NI; ++i)
<a name="l00045"></a>00045     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j &lt;= NJ; ++j)
<a name="l00046"></a>00046         T(i,j) = PL + (PR - PL) * i * coef;
<a name="l00047"></a>00047 }
<a name="l00048"></a>00048 
<a name="l00049"></a>00049 <span class="keywordtype">int</span> main() 
<a name="l00050"></a>00050 {
<a name="l00051"></a>00051   <span class="keywordtype">double</span> length_x, length_y, dt, tolerance = 1e-7; 
<a name="l00052"></a>00052   <span class="keywordtype">int</span> num_nodes_x, num_nodes_y, frequency, tdma_iter = 2000;
<a name="l00053"></a>00053   <span class="keywordtype">double</span> porosity, viscosity, permeability, compresibility;
<a name="l00054"></a>00054   <span class="keywordtype">double</span> PL, PR, Tmax;
<a name="l00055"></a>00055 
<a name="l00056"></a>00056 <span class="comment">// Reading data from the input file</span>
<a name="l00057"></a>00057     std::ifstream input_cin (<span class="stringliteral">&quot;inputSingle2D&quot;</span>); 
<a name="l00058"></a>00058     input_cin &gt;&gt; length_x &gt;&gt; length_y
<a name="l00059"></a>00059               &gt;&gt; num_nodes_x &gt;&gt; num_nodes_y
<a name="l00060"></a>00060               &gt;&gt; porosity
<a name="l00061"></a>00061               &gt;&gt; permeability
<a name="l00062"></a>00062               &gt;&gt; viscosity
<a name="l00063"></a>00063               &gt;&gt; compresibility
<a name="l00064"></a>00064               &gt;&gt; PL
<a name="l00065"></a>00065               &gt;&gt; PR
<a name="l00066"></a>00066               &gt;&gt; dt
<a name="l00067"></a>00067               &gt;&gt; Tmax
<a name="l00068"></a>00068               &gt;&gt; frequency;
<a name="l00069"></a>00069     input_cin.close();
<a name="l00070"></a>00070 
<a name="l00071"></a>00071     Tmax += dt;
<a name="l00072"></a>00072 
<a name="l00073"></a>00073     <span class="keywordtype">double</span> Gamma = permeability / (porosity * viscosity * compresibility);
<a name="l00074"></a>00074 
<a name="l00075"></a>00075     std::cout &lt;&lt; <span class="stringliteral">&quot;\n Gamma = &quot;</span> &lt;&lt; Gamma;
<a name="l00076"></a>00076 
<a name="l00077"></a>00077     <a class="code" href="classTuna_1_1StructuredMesh.html" title="General structured meshes on rectangular domains.">StructuredMesh&lt;Uniform&lt;double, 2&gt;</a> &gt; mesh(length_x, num_nodes_x,
<a name="l00078"></a>00078                                              length_y, num_nodes_y);
<a name="l00079"></a>00079     <span class="keywordtype">double</span> dx = mesh.getDelta(X), dy = mesh.getDelta(Y);
<a name="l00080"></a>00080     mesh.print();
<a name="l00081"></a>00081     ScalarField2D p ( mesh.getExtentVolumes() );
<a name="l00082"></a>00082     ScalarField2D pa( mesh.getExtentNodes()   ); 
<a name="l00083"></a>00083     ScalarField2D pn( mesh.getExtentNodes()   );
<a name="l00084"></a>00084 
<a name="l00085"></a>00085 
<a name="l00086"></a>00086     pn = 1.0; <span class="comment">// initial condition on nodes</span>
<a name="l00087"></a>00087     pa = 1.0; <span class="comment">// initial condition on nodes</span>
<a name="l00088"></a>00088     p = 1.0; <span class="comment">// initial condition on volumes</span>
<a name="l00089"></a>00089 
<a name="l00090"></a>00090     exactSolution(pn, length_x, dx, PL, PR);
<a name="l00091"></a>00091     NumUtils::interpolateToVolumes(pa, pn);
<a name="l00092"></a>00092 
<a name="l00093"></a>00093     Range all = Range::all();
<a name="l00094"></a>00094     p(0, all) = 2.0;
<a name="l00095"></a>00095     pn(0, all) = 2.0; <span class="comment">// boundary condition</span>
<a name="l00096"></a>00096 
<a name="l00097"></a>00097     InOut::writeToFile_DX(pn, 0, <span class="stringliteral">&quot;./DataSingle2D/pres.&quot;</span>, dx, dy);
<a name="l00098"></a>00098        
<a name="l00099"></a>00099     SparseMatrix&lt; Diagonal&lt; double, 2&gt; &gt; A(num_nodes_x, num_nodes_y); 
<a name="l00100"></a>00100     ScalarField2D              b(num_nodes_x, num_nodes_y);
<a name="l00101"></a>00101 
<a name="l00102"></a>00102     <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt; CDS&lt;double, 2&gt;</a> &gt; single_phase(p, A, b, mesh.getDeltas());
<a name="l00103"></a>00103     single_phase.setDeltaTime(dt); 
<a name="l00104"></a>00104     single_phase.setGamma(Gamma);
<a name="l00105"></a>00105     single_phase.setDirichlet(LEFT_WALL); 
<a name="l00106"></a>00106     single_phase.setDirichlet(RIGHT_WALL);
<a name="l00107"></a>00107     single_phase.setNeumann(TOP_WALL);
<a name="l00108"></a>00108     single_phase.setNeumann(BOTTOM_WALL);
<a name="l00109"></a>00109     single_phase.print();
<a name="l00110"></a>00110 
<a name="l00111"></a>00111     ofstream error_fp(<span class="stringliteral">&quot;./DataSingle2D/error&quot;</span>), residual_fp(<span class="stringliteral">&quot;./DataSingle2D/residual&quot;</span>);
<a name="l00112"></a>00112     <span class="keywordtype">int</span> iteration = 0, Nerror = 0;
<a name="l00113"></a>00113     <span class="keywordtype">double</span> t = dt;
<a name="l00114"></a>00114     <span class="keywordtype">double</span> error = 1.0;
<a name="l00115"></a>00115     <span class="keywordtype">double</span> residual = 1.0;
<a name="l00116"></a>00116 
<a name="l00117"></a>00117     <span class="keywordflow">while</span> (t &lt;= Tmax) {
<a name="l00118"></a>00118       std::cout &lt;&lt; <span class="stringliteral">&quot;\n ---- Iteration &quot;</span> &lt;&lt; ++iteration 
<a name="l00119"></a>00119                 &lt;&lt; <span class="stringliteral">&quot;\t time = &quot;</span> &lt;&lt; t
<a name="l00120"></a>00120                 &lt;&lt; <span class="stringliteral">&quot;\t Res = &quot;</span> &lt;&lt; residual
<a name="l00121"></a>00121                 &lt;&lt; <span class="stringliteral">&quot;\t Err = &quot;</span> &lt;&lt; error;
<a name="l00122"></a>00122       single_phase.calcCoefficients();
<a name="l00123"></a>00123       Solver::TDMA2DX(single_phase, tolerance, tdma_iter, 1.0);
<a name="l00124"></a>00124       residual = single_phase.calcResidual();
<a name="l00125"></a>00125       <span class="comment">//      error = single_phase.calcErrorL1();</span>
<a name="l00126"></a>00126 
<a name="l00127"></a>00127       <span class="comment">//      residual_fp &lt;&lt; iteration &lt;&lt; &quot;\t&quot; &lt;&lt; residual &lt;&lt; std::endl;        </span>
<a name="l00128"></a>00128       residual_fp &lt;&lt; dt * iteration &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; residual &lt;&lt; std::endl;   
<a name="l00129"></a>00129  
<a name="l00130"></a>00130       single_phase.update();
<a name="l00131"></a>00131 
<a name="l00132"></a>00132       <span class="comment">/* */</span>
<a name="l00133"></a>00133       error = 0.0;
<a name="l00134"></a>00134       Nerror = 0;
<a name="l00135"></a>00135       NumUtils::interpolateToNodes(pn, p);
<a name="l00136"></a>00136       <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = pn.lbound(firstDim)+1; i &lt;= pn.ubound(firstDim)-1; ++i)
<a name="l00137"></a>00137         <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = pn.lbound(secondDim)+1; j &lt;= pn.ubound(secondDim)-1; ++j) {
<a name="l00138"></a>00138 
<a name="l00139"></a>00139           <span class="comment">// L_2</span>
<a name="l00140"></a>00140           error += (pn(i,j) - pa(i,j)) * (pn(i,j) - pa(i,j));
<a name="l00141"></a>00141           Nerror++;
<a name="l00142"></a>00142           <span class="comment">// L_1</span>
<a name="l00143"></a>00143           <span class="comment">//      if ( fabs( pn(i,j) - pa(i,j) ) &gt; error )</span>
<a name="l00144"></a>00144           <span class="comment">//        error = fabs (  pn(i,j) - pa(i,j) );</span>
<a name="l00145"></a>00145         }
<a name="l00146"></a>00146       error = sqrt(error) / Nerror;
<a name="l00147"></a>00147       <span class="comment">//      error_fp &lt;&lt; iteration &lt;&lt; &quot;\t&quot; &lt;&lt; error &lt;&lt; std::endl;</span>
<a name="l00148"></a>00148       error_fp &lt;&lt; dt * iteration &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; error &lt;&lt; std::endl;
<a name="l00149"></a>00149       <span class="comment">/* */</span>
<a name="l00150"></a>00150 
<a name="l00151"></a>00151       t += dt;
<a name="l00152"></a>00152 
<a name="l00153"></a>00153       <span class="comment">/*  */</span>
<a name="l00154"></a>00154       <span class="keywordflow">if</span> ( !(iteration % frequency) ) {
<a name="l00155"></a>00155         NumUtils::interpolateToNodes(pn, p);
<a name="l00156"></a>00156         InOut::writeToFile_DX(pn, iteration, <span class="stringliteral">&quot;./DataSingle2D/pres.&quot;</span>,dx, dy);    
<a name="l00157"></a>00157       }
<a name="l00158"></a>00158       <span class="comment">/* */</span>
<a name="l00159"></a>00159     }
<a name="l00160"></a>00160 
<a name="l00161"></a>00161     std::cout &lt;&lt; <span class="stringliteral">&quot;\n\n NOTE: The data were written in the [./DataSingle2D] directory \n\n&quot;</span>;
<a name="l00162"></a>00162     <span class="keywordflow">return</span> 0;
<a name="l00163"></a>00163 }
<a name="l00164"></a>00164 
<a name="l00165"></a>00165 
<a name="l00166"></a>00166 
<a name="l00167"></a>00167 
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